Fix gyroscopic precession sign: roll term, not pitch

The propeller gyroscopic torque had the wrong sign on the ROLL axis (row 0 of
torque_inertia), in both dynamics (numeric) and symbolic_dynamics.

The gyroscopic torque is -ω × h with net rotor angular momentum h = h_z·ẑ,
giving (-q·h_z, +p·h_z, 0): the roll and pitch rows must have OPPOSITE signs.
The subtlety is that S = Σ mixing_matrix[-1]·ω_rotor uses the yaw-torque-direction
row, i.e. the NEGATIVE of the physical spin, so h_z = -prop_inertia·S. Hence:
  roll  (x) = -q·h_z = +prop_inertia·ang_vel[1]·S   (code had a leading '-', the bug)
  pitch (y) = +p·h_z = -prop_inertia·ang_vel[0]·S   (code was already correct)
The z (spin-up/down reaction) row is already correct, and is in fact what pins
the convention: it is consistent only with spin = -mixing_matrix[-1].

Verified against -ω × h to machine precision on all axes; numeric == symbolic
still holds for ang_vel_dot. Only matters for non-negligible prop_inertia /
larger quads during yaw-type maneuvers; negligible for a Crazyflie.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

Author: Zaffer

crazyflow/dynamics/first_principles/dynamics.py

@@ -139,9 +139,17 @@ def dynamics(
     rotor_vel_dot_rads = (
         rotor_vel_dot * rpm_to_rad if rotor_vel_dot is not None else xp.zeros_like(rotor_vel)
     )
+    # Gyroscopic torque -ω × h, with net rotor angular momentum h = h_z·ẑ.
+    # -ω × (0,0,h_z) = (-q·h_z, +p·h_z, 0): the roll and pitch rows have OPPOSITE signs.
+    # Here S = Σ mixing_matrix[-1]·ω_rotor is the yaw-torque-direction sum, i.e. the NEGATIVE of
+    # the physical spin direction (same row used, correctly, for the drag reaction torque and the
+    # z row below). Hence h_z = -prop_inertia·S, and substituting:
+    #   roll  (x) = -q·h_z = +prop_inertia·ang_vel[1]·S
+    #   pitch (y) = +p·h_z = -prop_inertia·ang_vel[0]·S
+    # The z row is the spin-up/down reaction torque.
     torque_inertia = prop_inertia * xp.stack(
         [
-            -ang_vel[..., 1] * xp.sum(mixing_matrix[..., -1, :] * rotor_vel_rads, axis=-1),
+            ang_vel[..., 1] * xp.sum(mixing_matrix[..., -1, :] * rotor_vel_rads, axis=-1),
             -ang_vel[..., 0] * xp.sum(mixing_matrix[..., -1, :] * rotor_vel_rads, axis=-1),
             xp.sum(mixing_matrix[..., -1, :] * rotor_vel_dot_rads, axis=-1),
         ],
@@ -260,8 +268,11 @@ def symbolic_dynamics(
     rpm_to_rad = 2 * cs.pi / 60
     rotor_vel_rads = symbols.rotor_vel * rpm_to_rad
     rotor_vel_dot_rads = rotor_vel_dot * rpm_to_rad if model_rotor_vel else symbols.rotor_vel * 0.0
+    # Gyroscopic torque -ω × h (see dynamics() for the full derivation): the roll row is
+    # +ang_vel[1]·S and the pitch row is -ang_vel[0]·S (opposite signs), where S uses the
+    # yaw-torque-direction row (= -physical spin), so h_z = -prop_inertia·S.
     torque_inertia = prop_inertia * cs.vertcat(
-        -symbols.ang_vel[1] * cs.sum(mixing_matrix[-1, :] * rotor_vel_rads),
+        symbols.ang_vel[1] * cs.sum(mixing_matrix[-1, :] * rotor_vel_rads),
         -symbols.ang_vel[0] * cs.sum(mixing_matrix[-1, :] * rotor_vel_rads),
         cs.sum(mixing_matrix[-1, :] * rotor_vel_dot_rads),
     )